Ion conductor is used for an electrochemical cell such as a battery cell, a sensor or a fuel cell. A solid oxide electrolyte is used for the ion conductor. The solid oxide electrolyte is being widely used because the solid oxide electrolyte has high ion conductivity. The solid oxide electrolyte includes a BaCeO3-based perovskite electrolyte. For example, Patent Document 1 discloses an art where a part of Ce site is displaced with Zr, Ti or the like in order to improve chemical stability of the BaCeO3-based perovskite.    Patent Document 1: Japanese Patent Application Publication No. 2000-302550